带跳次分数布朗运动下亚式期权定价  

Asian Option Pricing Under Sub-Fractional Brownian Motion with Jump

作　　者：杨月 王永茂[1] YANG Yue;WANG Yong-mao(College of Science,Yanshan University,Qinhuangdao 066004,China)

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《数学的实践与认识》2020年第13期131-140,共10页Mathematics in Practice and Theory

基　　金：河北省自然科学基金青年基金(F2017203130)。

摘　　要：研究次分数布朗运动环境下带跳跃的几何亚式期权定价问题,给出了标的资产遵循次分数跳-扩散过程下的几何平均亚式期权的定价公式.首先,将次分数公式推广到次分数跳-扩散的情况;其次,结合自融资交易策略得到次分数布朗运动下带跳的几何平均亚式期权满足的Black-Scholes偏微分方程;最后,利用变量替换法求解该偏微分方程得出亚式期权的定价公式.通过数值实验,可以看出赫斯特指数和跳跃强度对亚式期权价值有显著的影响.推广了一些已有的结论,扩展了期权定价相关理论.In this paper,we study the pricing problems of geometric Asian option with jump under sub-fractional Brownian motion.We give an analytical solution for the pricing of geometric average Asian option under sub-fractional jump-diffusion process.Firstly,the sub-fractional Ito formula is extended to the condition of sub-fractional jump-diffusion.Then,the Black-Scholes partial differential equation of geometrically average Asian option pricing with jump under sub-fractional Brownian motion is obtained by combining the self-financing trad?ing strategy.Finally,the pricing formula of Asian option is obtained by solving the partial differential equation with variable replacement method.Through numerical simulation,it is concluded that Hurst index and jump intensity have significant effects on the value of Asian options.This paper generalizes some existing conclusions and extends the theory of option pricing.

关 键 词：次分数跳-扩散过程 几何平均亚式期权 Black-Scholes偏微分方程 

分 类 号：F830.9[经济管理—金融学] O211.6[理学—概率论与数理统计]